Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
545 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 545 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#5116 | C2 | semidirect |
| 3. C2×#63547 | C2 | semidirect |
| 4. #10589415 | C2 | semidirect |
| 5. #10589114 | C2 | semidirect |
| 11. C2×C3×Dic12 | C22 | semidirect |
| 15. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 16. C3×#818 | C22 | semidirect |
| 24. #5116 | D3 | semidirect |
| 60. C2×Dic12 | C2×D3 | semidirect |
| 68. #818 | C2×D3 | semidirect |
| 139. C22×C32 | SD32 | semidirect |
| 239. C22×C3 | #827 | semidirect |
| 240. C22×C3 | #828 | semidirect |
| 260. C32 | #2187 | semidirect |
| 299. C22 | #63547 | semidirect |
| 307. C3 | #71085 | semidirect |
| 308. C3 | #72036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D24 | 2 |
| C3×#5116 | 2 |
| C2×#63547 | 2 |
| #10589415 | 2 |
| #10589114 | 2 |
| #72036 | 3 |
| #71085 | 3 |